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harina [27]
3 years ago
11

Best answer gets brainly

Mathematics
2 answers:
seropon [69]3 years ago
8 0
Go in this order: true true false true false
SSSSS [86.1K]3 years ago
5 0
T,t,f,t,t I’m sure of it
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Evaluate the line integral by the two following methods. xy dx + x2 dy C is counterclockwise around the rectangle with vertices
Airida [17]

Answer:

25/2

Step-by-step explanation:

Recall that for a parametrized differentiable curve C = (x(t), y(t)) with the parameter t varying on some interval [a, b]

\large \displaystyle\int_{C}[P(x,y)dx+Q(x,y)dy]=\displaystyle\int_{a}^{b}[P(x(t),y(t))x'(t)+Q(x(t),y(t))y'(t)]dt

Where P, Q are scalar functions

We want to compute

\large \displaystyle\int_{C}P(x,y)dx+Q(x,y)dy=\displaystyle\int_{C}xydx+x^2dy

Where C is the rectangle with vertices (0, 0), (5, 0), (5, 1), (0, 1) going counterclockwise.

a) Directly

Let us break down C into 4 paths \large C_1,C_2,C_3,C_4 which represents the sides of the rectangle.

\large C_1 is the line segment from (0,0) to (5,0)

\large C_2 is the line segment from (5,0) to (5,1)

\large C_3 is the line segment from (5,1) to (0,1)

\large C_4 is the line segment from (0,1) to (0,0)

Then

\large \displaystyle\int_{C}=\displaystyle\int_{C_1}+\displaystyle\int_{C_2}+\displaystyle\int_{C_3}+\displaystyle\int_{C_4}

Given 2 points P, Q we can always parametrize the line segment from P to Q with

r(t) = tQ + (1-t)P for 0≤ t≤ 1

Let us compute the first integral. We parametrize \large C_1 as

r(t) = t(5,0)+(1-t)(0,0) = (5t, 0) for 0≤ t≤ 1 and

r'(t) = (5,0) so

\large \displaystyle\int_{C_1}xydx+x^2dy=0

 Now the second integral. We parametrize \large C_2 as

r(t) = t(5,1)+(1-t)(5,0) = (5 , t) for 0≤ t≤ 1 and

r'(t) = (0,1) so

\large \displaystyle\int_{C_2}xydx+x^2dy=\displaystyle\int_{0}^{1}25dt=25

The third integral. We parametrize \large C_3 as

r(t) = t(0,1)+(1-t)(5,1) = (5-5t, 1) for 0≤ t≤ 1 and

r'(t) = (-5,0) so

\large \displaystyle\int_{C_3}xydx+x^2dy=\displaystyle\int_{0}^{1}(5-5t)(-5)dt=-25\displaystyle\int_{0}^{1}dt+25\displaystyle\int_{0}^{1}tdt=\\\\=-25+25/2=-25/2

The fourth integral. We parametrize \large C_4 as

r(t) = t(0,0)+(1-t)(0,1) = (0, 1-t) for 0≤ t≤ 1 and

r'(t) = (0,-1) so

\large \displaystyle\int_{C_4}xydx+x^2dy=0

So

\large \displaystyle\int_{C}xydx+x^2dy=25-25/2=25/2

Now, let us compute the value using Green's theorem.

According with this theorem

\large \displaystyle\int_{C}Pdx+Qdy=\displaystyle\iint_{A}(\displaystyle\frac{\partial Q}{\partial x}-\displaystyle\frac{\partial P}{\partial y})dydx

where A is the interior of the rectangle.

so A={(x,y) |  0≤ x≤ 5,  0≤ y≤ 1}

We have

\large \displaystyle\frac{\partial Q}{\partial x}=2x\\\\\displaystyle\frac{\partial P}{\partial y}=x

so

\large \displaystyle\iint_{A}(\displaystyle\frac{\partial Q}{\partial x}-\displaystyle\frac{\partial P}{\partial y})dydx=\displaystyle\int_{0}^{5}\displaystyle\int_{0}^{1}xdydx=\displaystyle\int_{0}^{5}xdx\displaystyle\int_{0}^{1}dy=25/2

3 0
3 years ago
Find the cos A and tan B to four decimal places. URGENT
Nikolay [14]

cos A is 0.8511 and tan B is 1.6

Step-by-step explanation:

Find the 3rd length or the hypotenuse.

<u>Pythagoras theorem</u>

hypotenuse^{2} = adjacent^{2} + opposite^{2}

hypotenuse^{2} = 8^{2} + 5^{2}

hypotenuse^{2} = 64 + 25

hypotenuse = \sqrt{89}

hypotenuse = 9.4

a) Cos A

<u>Data:</u>

Adjacent = 8

Hypotenuse = 9.4

<u>Formula:</u>

Cos (Angle) = \frac{adjacent}{hypotenuse}

Cos A =  \frac{8}{9.4}

Cos A = 0.8511

A = cos^{-1} (0.8511)

A = 31.7°

b) Tan B

<u>Data: </u>

Opposite = 8

Adjacent = 5

<u>Formula:</u>

Tan (Angle) = \frac{opposite}{adjacent}

Tan B = \frac{8}{5}

Tan B = 1.6

B =  cos^{-1} (1.6)

B = 58°

Therefore, cos A is 0.8511 and tan B is 1.6.

Keyword: cos, tan

Learn more about cos at

  • brainly.com/question/5013374
  • brainly.com/question/9532142

#LearnwithBrainly

3 0
2 years ago
Find the measure of the missing angle using the triangle angle sum theorem
Greeley [361]

Answer:

m∠60

Step-by-step explanation:

30 + 90 = 120

180-120=60

7 0
3 years ago
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HELP
vaieri [72.5K]
4/8 simplified is 2/4 i think
3 0
3 years ago
Analyze the diagram below and complete the instructions that follow.
juin [17]

Answer:

Hello

Step-by-step explanation:

the Pythagoras Theorem proves this

7 0
3 years ago
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